{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "AU\\\\\n",
    "BU\n",
    "$$\n",
    "\n",
    "$$\n",
    "(\\frac{\\partial \\lambda_{0}}{\\partial x} A[i,:] + \\frac{\\partial \\lambda_{1}}{\\partial x} A[j,:] + \\frac{\\partial \\lambda_{2}}{\\partial x}A[k,:] + \\frac{\\partial \\lambda_{0}}{\\partial y}B[i, :] +\\frac{\\partial \\lambda_{1}}{\\partial y}B[j, :] + \\frac{\\partial \\lambda_{2}}{\\partial y}B[k, :])U\\\\\n",
    "$$\n",
    "\n",
    "$$\n",
    "GU\n",
    "$$\n",
    "\n",
    "在每个边界单元上， "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from IPython.display import display\n",
    "from sympy import *\n",
    "import numpy as np\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHQAAAAVBAMAAABlHNfrAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAy8Riwm56K5OAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$1.0 x e^{x} \\sin{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "       x       \n",
       "1.0⋅x⋅ℯ ⋅sin(x)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = 1/4*(sin(x)-x*cos(x))*x*exp(x)\n",
    "(diff(u, x, 2) - 2*diff(u,x)+2*u).simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x, y, z, w, s, c, r, zw= symbols('x, y, z, w, s, c, r, zw')\n",
    "a = atan2(y, x)\n",
    "b =sqrt(x**2+y**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "g1 = (1/(z-1)*sin((z-1)*w) - 1/(z+1)*sin((z+1)*w))*(cos((z-1)*a) - cos((z+1)*a))\n",
    "g2 = (1/(z-1)*sin((z-1)*a) - 1/(z+1)*sin((z+1)*a))*(cos((z-1)*w) - cos((z+1)*w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mJQXdpiB7t6oQEqoccuVTAOq9WbmUgk56/sfcQEilh8vTEtXLEf1MjayZNuYZfoMHT3sc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\n",
      "text/latex": [
       "$$r^{z + 1} \\left(\\left(- \\frac{1}{z + 1} \\sin{\\left (w \\left(z + 1\\right) \\right )} + \\frac{1}{z - 1} \\sin{\\left (w \\left(z - 1\\right) \\right )}\\right) \\left(\\cos{\\left (\\left(z - 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} - \\cos{\\left (\\left(z + 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )}\\right) - \\left(- \\frac{1}{z + 1} \\sin{\\left (\\left(z + 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} + \\frac{1}{z - 1} \\sin{\\left (\\left(z - 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )}\\right) \\left(\\cos{\\left (w \\left(z - 1\\right) \\right )} - \\cos{\\left (w \\left(z + 1\\right) \\right )}\\right)\\right) \\left(\\frac{r^{2} x^{2}}{x^{2} + y^{2}} - 1\\right)^{2} \\left(\\frac{r^{2} y^{2}}{x^{2} + y^{2}} - 1\\right)^{2}$$"
      ],
      "text/plain": [
       "                                                                              \n",
       "                                                                              \n",
       " z + 1 ⎛⎛  sin(w⋅(z + 1))   sin(w⋅(z - 1))⎞                                   \n",
       "r     ⋅⎜⎜- ────────────── + ──────────────⎟⋅(cos((z - 1)⋅atan2(y, x)) - cos((z\n",
       "       ⎝⎝      z + 1            z - 1     ⎠                                   \n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                      ⎛  sin((z + 1)⋅atan2(y, x))   sin((z - 1)⋅atan2(y, x))⎞ \n",
       " + 1)⋅atan2(y, x))) - ⎜- ──────────────────────── + ────────────────────────⎟⋅\n",
       "                      ⎝           z + 1                      z - 1          ⎠ \n",
       "                                                                              \n",
       "\n",
       "                                                2              2\n",
       "                                   ⎛  2  2     ⎞  ⎛  2  2     ⎞ \n",
       "                                 ⎞ ⎜ r ⋅x      ⎟  ⎜ r ⋅y      ⎟ \n",
       "(cos(w⋅(z - 1)) - cos(w⋅(z + 1)))⎟⋅⎜─────── - 1⎟ ⋅⎜─────── - 1⎟ \n",
       "                                 ⎠ ⎜ 2    2    ⎟  ⎜ 2    2    ⎟ \n",
       "                                   ⎝x  + y     ⎠  ⎝x  + y     ⎠ "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = g1 - g2\n",
    "u = (r**2*cos(theta)**2 - 1)**2*(r**2*sin(theta)**2 - 1)**2*r**(1+z)*g\n",
    "display(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "uxx = diff(u, x, 2)\n",
    "uyy = diff(u, y, 2)\n",
    "uxy = diff(diff(u, x), y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Oq2QHlRLHjEtj1L+x2WJ3TtB/zmalphsXFlF/Zon92Sha41bK5U/CTLWvTt2n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\nCqsWIU0kxl4IIKvs/v8HBKaHoT/zSI4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{\\left(x^{2} + y^{2}\\right)^{\\frac{z}{2} - \\frac{3}{2}} \\left(y^{2} - 1\\right)^{2}}{\\left(z - 1\\right) \\left(z + 1\\right)} \\left(- 8 x y \\left(x^{2} - 1\\right) \\left(x^{2} + y^{2}\\right) \\left(- \\frac{4 y \\sin{\\left (w \\right )}}{\\sqrt{x^{2} + y^{2}}} \\left(z - 1\\right) \\left(z + 1\\right) \\sin{\\left (w z \\right )} \\sin{\\left (z \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} + \\left(\\left(z - 1\\right) \\sin{\\left (w \\left(z + 1\\right) \\right )} - \\left(z + 1\\right) \\sin{\\left (w \\left(z - 1\\right) \\right )}\\right) \\left(\\left(z - 1\\right) \\sin{\\left (\\left(z - 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} - \\left(z + 1\\right) \\sin{\\left (\\left(z + 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )}\\right)\\right) - 2 x \\left(x^{2} - 1\\right)^{2} \\left(z + 1\\right) \\left(x \\left(z + 1\\right) \\left(\\frac{y}{\\sqrt{x^{2} + y^{2}}} \\left(\\left(z - 1\\right) \\sin{\\left (w \\left(z + 1\\right) \\right )} - \\left(z + 1\\right) \\sin{\\left (w \\left(z - 1\\right) \\right )}\\right) \\sin{\\left (z \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} - \\left(\\left(z - 1\\right) \\sin{\\left (\\left(z + 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} - \\left(z + 1\\right) \\sin{\\left (\\left(z - 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )}\\right) \\sin{\\left (w \\right )} \\sin{\\left (w z \\right )}\\right) + 2 x \\left(- \\frac{y}{\\sqrt{x^{2} + y^{2}}} \\left(\\left(z - 1\\right) \\sin{\\left (w \\left(z + 1\\right) \\right )} - \\left(z + 1\\right) \\sin{\\left (w \\left(z - 1\\right) \\right )}\\right) \\sin{\\left (z \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} + \\left(\\left(z - 1\\right) \\sin{\\left (\\left(z + 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} - \\left(z + 1\\right) \\sin{\\left (\\left(z - 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )}\\right) \\sin{\\left (w \\right )} \\sin{\\left (w z \\right )}\\right) + y \\left(- \\frac{4 y \\sin{\\left (w \\right )}}{\\sqrt{x^{2} + y^{2}}} \\left(z - 1\\right) \\left(z + 1\\right) \\sin{\\left (w z \\right )} \\sin{\\left (z \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} + \\left(\\left(z - 1\\right) \\sin{\\left (w \\left(z + 1\\right) \\right )} - \\left(z + 1\\right) \\sin{\\left (w \\left(z - 1\\right) \\right )}\\right) \\left(\\left(z - 1\\right) \\sin{\\left (\\left(z - 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} - \\left(z + 1\\right) \\sin{\\left (\\left(z + 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )}\\right)\\right)\\right) + y \\left(x^{2} - 1\\right)^{2} \\left(- \\frac{4 y \\sin{\\left (w \\right )}}{\\sqrt{x^{2} + y^{2}}} \\left(z - 1\\right) \\left(z + 1\\right) \\left(3 x \\sin{\\left (z \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} + y z \\cos{\\left (z \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )}\\right) \\sin{\\left (w z \\right )} + \\left(\\left(z - 1\\right) \\sin{\\left (w \\left(z + 1\\right) \\right )} - \\left(z + 1\\right) \\sin{\\left (w \\left(z - 1\\right) \\right )}\\right) \\left(2 x \\left(z - 1\\right) \\sin{\\left (\\left(z - 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} - 2 x \\left(z + 1\\right) \\sin{\\left (\\left(z + 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} + y \\left(z - 1\\right)^{2} \\cos{\\left (\\left(z - 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} - y \\left(z + 1\\right)^{2} \\cos{\\left (\\left(z + 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )}\\right)\\right) - 2 \\left(x^{2} - 1\\right) \\left(x^{2} + y^{2}\\right) \\left(9 x^{2} - 1\\right) \\left(z + 1\\right) \\left(\\frac{y}{\\sqrt{x^{2} + y^{2}}} \\left(\\left(z - 1\\right) \\sin{\\left (w \\left(z + 1\\right) \\right )} - \\left(z + 1\\right) \\sin{\\left (w \\left(z - 1\\right) \\right )}\\right) \\sin{\\left (z \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} - \\left(\\left(z - 1\\right) \\sin{\\left (\\left(z + 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} - \\left(z + 1\\right) \\sin{\\left (\\left(z - 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )}\\right) \\sin{\\left (w \\right )} \\sin{\\left (w z \\right )}\\right) - 8 \\left(x^{2} + y^{2}\\right)^{2} \\left(3 x^{2} - 1\\right) \\left(\\frac{y}{\\sqrt{x^{2} + y^{2}}} \\left(\\left(z - 1\\right) \\sin{\\left (w \\left(z + 1\\right) \\right )} - \\left(z + 1\\right) \\sin{\\left (w \\left(z - 1\\right) \\right )}\\right) \\sin{\\left (z \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} - \\left(\\left(z - 1\\right) \\sin{\\left (\\left(z + 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )} - \\left(z + 1\\right) \\sin{\\left (\\left(z - 1\\right) \\operatorname{atan_{2}}{\\left (y,x \\right )} \\right )}\\right) \\sin{\\left (w \\right )} \\sin{\\left (w z \\right )}\\right)\\right)$$"
      ],
      "text/plain": [
       "         z   3                                                                \n",
       "         ─ - ─                                                                \n",
       "         2   2         2 ⎛                                                    \n",
       "⎛ 2    2⎞      ⎛ 2    ⎞  ⎜        ⎛ 2    ⎞ ⎛ 2    2⎞ ⎛  4⋅y⋅(z - 1)⋅(z + 1)⋅si\n",
       "⎝x  + y ⎠     ⋅⎝y  - 1⎠ ⋅⎜- 8⋅x⋅y⋅⎝x  - 1⎠⋅⎝x  + y ⎠⋅⎜- ──────────────────────\n",
       "                         ⎜                           ⎜                        \n",
       "                         ⎜                           ⎜                        \n",
       "                         ⎝                           ⎝                       ╲\n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "n(w)⋅sin(w⋅z)⋅sin(z⋅atan2(y, x))                                              \n",
       "──────────────────────────────── + ((z - 1)⋅sin(w⋅(z + 1)) - (z + 1)⋅sin(w⋅(z \n",
       "  _________                                                                   \n",
       " ╱  2    2                                                                    \n",
       "╱  x  + y                                                                     \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                            ⎞ \n",
       "- 1)))⋅((z - 1)⋅sin((z - 1)⋅atan2(y, x)) - (z + 1)⋅sin((z + 1)⋅atan2(y, x)))⎟ \n",
       "                                                                            ⎟ \n",
       "                                                                            ⎟ \n",
       "                                                                            ⎠ \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "              2                                                               \n",
       "      ⎛ 2    ⎞          ⎛          ⎛y⋅((z - 1)⋅sin(w⋅(z + 1)) - (z + 1)⋅sin(w⋅\n",
       "- 2⋅x⋅⎝x  - 1⎠ ⋅(z + 1)⋅⎜x⋅(z + 1)⋅⎜──────────────────────────────────────────\n",
       "                        ⎜          ⎜                                _________ \n",
       "                        ⎜          ⎜                               ╱  2    2  \n",
       "                        ⎝          ⎝                             ╲╱  x  + y   \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "(z - 1)))⋅sin(z⋅atan2(y, x))                                                  \n",
       "──────────────────────────── - ((z - 1)⋅sin((z + 1)⋅atan2(y, x)) - (z + 1)⋅sin\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                      ⎞       ⎛  y⋅((z - 1)⋅sin(w⋅(z + 1)) - (\n",
       "((z - 1)⋅atan2(y, x)))⋅sin(w)⋅sin(w⋅z)⎟ + 2⋅x⋅⎜- ─────────────────────────────\n",
       "                                      ⎟       ⎜                               \n",
       "                                      ⎟       ⎜                               \n",
       "                                      ⎠       ⎝                               \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "z + 1)⋅sin(w⋅(z - 1)))⋅sin(z⋅atan2(y, x))                                     \n",
       "───────────────────────────────────────── + ((z - 1)⋅sin((z + 1)⋅atan2(y, x)) \n",
       "   _________                                                                  \n",
       "  ╱  2    2                                                                   \n",
       "╲╱  x  + y                                                                    \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                   ⎞     ⎛  4⋅y⋅(z - 1)⋅(z + 1\n",
       "- (z + 1)⋅sin((z - 1)⋅atan2(y, x)))⋅sin(w)⋅sin(w⋅z)⎟ + y⋅⎜- ──────────────────\n",
       "                                                   ⎟     ⎜                    \n",
       "                                                   ⎟     ⎜                    \n",
       "                                                   ⎠     ⎝                    \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       ")⋅sin(w)⋅sin(w⋅z)⋅sin(z⋅atan2(y, x))                                          \n",
       "──────────────────────────────────── + ((z - 1)⋅sin(w⋅(z + 1)) - (z + 1)⋅sin(w\n",
       "      _________                                                               \n",
       "     ╱  2    2                                                                \n",
       "   ╲╱  x  + y                                                                 \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "⋅(z - 1)))⋅((z - 1)⋅sin((z - 1)⋅atan2(y, x)) - (z + 1)⋅sin((z + 1)⋅atan2(y, x)\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                 (z - 1)⋅(z + 1)                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                 2                                                            \n",
       "  ⎞⎞     ⎛ 2    ⎞  ⎛  4⋅y⋅(z - 1)⋅(z + 1)⋅(3⋅x⋅sin(z⋅atan2(y, x)) + y⋅z⋅cos(z⋅\n",
       "))⎟⎟ + y⋅⎝x  - 1⎠ ⋅⎜- ────────────────────────────────────────────────────────\n",
       "  ⎟⎟               ⎜                                          _________       \n",
       "  ⎟⎟               ⎜                                         ╱  2    2        \n",
       "  ⎠⎠               ⎝                                       ╲╱  x  + y         \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "atan2(y, x)))⋅sin(w)⋅sin(w⋅z)                                                 \n",
       "───────────────────────────── + ((z - 1)⋅sin(w⋅(z + 1)) - (z + 1)⋅sin(w⋅(z - 1\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "    ⎛                                                                         \n",
       ")))⋅⎝2⋅x⋅(z - 1)⋅sin((z - 1)⋅atan2(y, x)) - 2⋅x⋅(z + 1)⋅sin((z + 1)⋅atan2(y, x\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "              2                                     2                         \n",
       ")) + y⋅(z - 1) ⋅cos((z - 1)⋅atan2(y, x)) - y⋅(z + 1) ⋅cos((z + 1)⋅atan2(y, x))\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "⎞⎞     ⎛ 2    ⎞ ⎛ 2    2⎞ ⎛   2    ⎞         ⎛y⋅((z - 1)⋅sin(w⋅(z + 1)) - (z +\n",
       "⎠⎟ - 2⋅⎝x  - 1⎠⋅⎝x  + y ⎠⋅⎝9⋅x  - 1⎠⋅(z + 1)⋅⎜────────────────────────────────\n",
       " ⎟                                           ⎜                                \n",
       " ⎟                                           ⎜                               ╱\n",
       " ⎠                                           ⎝                             ╲╱ \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       " 1)⋅sin(w⋅(z - 1)))⋅sin(z⋅atan2(y, x))                                        \n",
       "────────────────────────────────────── - ((z - 1)⋅sin((z + 1)⋅atan2(y, x)) - (\n",
       "_________                                                                     \n",
       "  2    2                                                                      \n",
       " x  + y                                                                       \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                               2              \n",
       "                                                ⎞     ⎛ 2    2⎞  ⎛   2    ⎞ ⎛y\n",
       "z + 1)⋅sin((z - 1)⋅atan2(y, x)))⋅sin(w)⋅sin(w⋅z)⎟ - 8⋅⎝x  + y ⎠ ⋅⎝3⋅x  - 1⎠⋅⎜─\n",
       "                                                ⎟                           ⎜ \n",
       "                                                ⎟                           ⎜ \n",
       "                                                ⎠                           ⎝ \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "⋅((z - 1)⋅sin(w⋅(z + 1)) - (z + 1)⋅sin(w⋅(z - 1)))⋅sin(z⋅atan2(y, x))         \n",
       "───────────────────────────────────────────────────────────────────── - ((z - \n",
       "                               _________                                      \n",
       "                              ╱  2    2                                       \n",
       "                            ╲╱  x  + y                                        \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "1)⋅sin((z + 1)⋅atan2(y, x)) - (z + 1)⋅sin((z - 1)⋅atan2(y, x)))⋅sin(w)⋅sin(w⋅z\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "\n",
       "   \n",
       "   \n",
       "  ⎞\n",
       " ⎞⎟\n",
       ")⎟⎟\n",
       " ⎟⎟\n",
       " ⎟⎟\n",
       " ⎠⎠\n",
       "───\n",
       "   "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "uxx.subs({sin(z*a):s, cos(z*a):c, sqrt(x**2+y**2):r})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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